LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	530.15
Title	Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model ([EBook]) / by Makoto Katori.
Author	Katori, Makoto
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2016.
Publication	Singapore : : Springer Singapore : : Imprint: Springer, , 2016.
Physical Details	X, 141 p. 16 illus. in color. : online resource.
Series	SpringerBriefs in Mathematical Physics 2197-1757 ; ; 11
ISBN	9789811002755
Summary Note	The purpose of this book is to introduce two recent topics in mathematical physics and probability theory: the Schramm–Loewner evolution (SLE) and interacting particle systems related to random matrix theory. A typical example of the latter systems is Dyson's Brownian motion (BM) model. The SLE and Dyson's BM model may be considered as "children" of the Bessel process with parameter D, BES(D), and the SLE and Dyson's BM model as "grandchildren" of BM. In Chap. 1 the parenthood of BM in diffusion processes is clarified and BES(D) is defined for any D ≥ 1. Dependence of the BES(D) path on its initial value is represented by the Bessel flow. In Chap. 2 SLE is introduced as a complexification of BES(D). Rich mathematics and physics involved in SLE are due to the nontrivial dependence of the Bessel flow on D. From a result for the Bessel flow, Cardy's formula in Carleson's form is derived for SLE. In Chap. 3 Dyson's BM model with parameter β is introduced as a multivariate extension of BES(D) with the relation D = β + 1. The book concentrates on the case where β = 2 and calls this case simply the Dyson model. The Dyson model inherits the two aspects of BES(3); hence it has very strong solvability. That is, the process is proved to be determinantal in the sense that all spatio-temporal correlation functions are given by determinants, and all of them are controlled by a single function called the correlation kernel. From the determinantal structure of the Dyson model, the Tracy–Widom distribution is derived. .:
Contents note	Preface -- 1 Bessel Process -- 2 Schramm-Loewner Evolution (SLE) -- 3 Dyson Model -- References -- Solutions -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-981-10-0275-5
Links to Related Works	Subject References: Dynamical Systems . Mathematical Physics . Mathematics . Probabilities . Probability theory and stochastic processes . Statistical Physics . Statistical Physics, Dynamical Systems and Complexity . Authors: Katori, Makoto . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematical Physics . Classification: 530.15 .

Catalogue Display

Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model

Reviews